@sebbotimpt Agreed. Often I read a section and go 'wait what about X?' and then someone who had the same problem as me explains it, or someone explains it to them. It's like a big, informal study group :D
#feedback I wish there was a diagram at the end of this lesson with all the conditionals and their negations. It would be helpful to have an overall visual comparison.
A few things for the structure of the intersectional relationships lessons --
1. can there be more visual representations
2. since the no contrapositive rule applies to all intersectional indicators, can it be right before the negation lesson-- (that also might highlight the distinction between negation and contrapositives better...)
3. can there be a final "value line" of where the bounds (lower and upper) of the statements apply -- i.e. None-some-------most------all. I think this helped me to best see the relationships among these intersectional indicators...
#feedback Yeah, I didn't even think of it until your comment, but the spacing between the negation and contrapositive lessons make it harder for those concepts to click and make it harder to recognize their distinction.
So negating isn’t saying no to the argument, it’s just saying “you forgot to look at it this way.” If you’re saying “it’s not the case that some unicorns poop rainbows,” then what you’re saying is there are no unicorns that poop rainbows. If not some, then none. You can’t say “if not some then most” because that’s not negating but adding onto the original claim. You can’t say “if not some then all” because again, that’s saying more than what the claim gives you evidence for.
Instead, negating is just saying “aha you forgot that there are some unicorns that DON’T poop rainbows!” A better view, for me, of negation is not “denying” or “negating” the original claim, but thinking of the possibilities that the claim didn’t originally consider.
Hi all, I made another flashcard set. This time for memorizing Quantifiers. Flashcards are what really helped me in undergrad and so I decided to make them to companion my 7sage studies. Thought I'd share to help others who would benefit :) made a folder that I will most likely add more sets to as I go. Much Love and happy studying! https://quizlet.com/user/ehoffmanwallace/folders/lsat-7sage-flashcards
@garrettgrahm I find it most helpful for necessary assumption questions. Negating the ACs can help you determine which negation would destroy/weaken the argument (that would indicate the assumption that the argument depends on).
I'm confused why the negation for 'some' changed in this lesson. In the previous lesson, it was said that the negation of 'some' is 'none'. In this lesson, the example above "Some unicorns poop rainbows" is negated to "Some unicorns don't poop rainbows". I don't understand the distinction here, #help
The lesson says that "Some unicorns don't poop rainbows" is a "tempting but incorrect negation". The correct negation is identified as "No unicorns poop rainbows", which is the same as "None of the unicorns poop rainbows."
Wait. Some unicorns poop rainbows is negated to No unicorns poop rainbows and is shown as (U->/PR). Wouldn't it be shown as /U->PR? This doesn't make total sense to me.
"No" would mean you have to negate a concept and make that concept the necessary condition. So "no unicorns poop rainbows" is equivalent to U->/PR.
/U->PR is the same as saying "if one is not a unicorn, then one poops rainbows.," which doesn't follow from the claim because we don't know anything about non-unicorns.
wait so are "some," "most, "many," quantifiers also conditionals? i.e. is "some unicorns dont poop rainbows" a conditional statement? or is it something completely different #help
@rc39 the quantifier words help identify the scope of the conditional. your if/then statement is your conditional, but the quantifier just specifies how often it occurs, or how much of any group is included within the conditional.
the statement "some unicorns don't poop rainbows" is a conditional statement, but the quantifier itself is not a conditional.
@tteokkim surgical explanation and i really appreciate it. you helped clarify some confusion working through this section. We may be looking at a conditional, but the quantifier is NOT conditional--it expresses an intersection. THANK YOU!
I believe if you insert "It's not the case that..." then that should negate it. For example, the negation of "Most Japanese whiskeys are expensive" would be "It's not the case that most Japanese whiskeys are expensive", which establishes an upper bound of 50%.
Or is the “tempting but incorrect negation” not saying that the above mentioned is incorrect, but the following statement is??? Lord, ima have a seizure 😂
What is an example of a question type we will encounter where having the negation of an intersection question is going to help us identify the correct answer?
"All" must include "most," because it's everything. That is always the case when the term "all" is used. However, the range for "must" has a lower boundary of "more than half" and an upper boundary of "all."
So while it's possible that "most" is actually referring to "all," it is not always the case. Therefore, JW -m→ E, leaves the possibility that all Japanese whiskeys are expensive, but does not guarantee it.
No, the negation of most is simply not most. There's a lesson where they go into it, but most implies in a hefty margin that something is greater than 50% and possibly by a larger share than that.
We can picture it on a rough scale of "50% < x <= 100%", where most is greater than half and can technically be all.
Few, on the other hand, implies that it is more than one (or possibly two, it's very vague) and less than one half. This is because few implies a really weird definition of "some but not many", a definition which highlights a more constricted view. With this, we can pinpoint a scale of "1 or 2 < x < many", with a rough indicator on your interpretation of many. However, this indication typically means it is less than half, so you could write the scale as "1 or 2 < x < 50%".
When looking at this, although a mathematical view could imply the negation of most as few, after all, "1 - 'most'" would leave you with a minority, there is a vague margin on what that would actually mean. As well, few is not inclusive to 1/2, meaning defining the negation of many as "few" would confuse an opposite for a negation.
Think back to the really early example of "the room is hot". The opposite of that statement would be "the room is cold", but would that be the negation? There's a range of temperatures that are not hot, like lukewarm, chilly, or freezing that aren't hot, and definitely aren't a strict cold. Because of this, the negation of "the room is hot" is simply "the room is not hot".
Think of the examples of most in a similar manner, where the negation of us saying "most penguins wear tuxedos" could not be "few penguins wear tuxedos". The language simply isn't inclusive to other possibilities, where no penguins wear tuxedos or exactly half of the penguins wear tuxedos. The only reasonable resolution is that it isn't the case that most penguins wear tuxedos.
TDLR: Few isn't inclusive to other possibilities in the range that the negation of most requires, but could be interpreted as an opposite, just not a negation.
since "all A are B" already includes the possibility of "some A are B" (because some could include all), so your answer would not entirely negate it.
additionally, I think that "many A are B" negated is just /(A ‑m→B), or, "it is not the case that many A are B". This way it doesn't necessitate that some A are not B, as the word "few" would.
The contrapositive of a conditional statement is created by flipping the order of the statement and negating both parts. It is logically equivalent to the original — meaning if one is true, so is the other.
On the other hand, negation simply means stating that the original statement is not true. It is not logically equivalent — instead, it expresses the opposite.
So, while the contrapositive preserves the truth of the original statement, negation challenges or contradicts it.
I still have a question. Do "all" statements always negate differently than group 1 conditional indicator statements? From my understanding of the material, this is how an all statement negates:
A some arrow /B
And this is how a conditional statement negates:
A and /B
But I think where I'm still confused is whether these are interchangeable since all is a group 1 indicator? I just want to know, if I see a group 1 indicator or an all statement on the LSAT, which translation I should use to get the right answer of if using either is fine.
During the skill builder exercises, the all statements where negated with both the some arrow and the and /, so I am guessing he's trying to say that both are correct. Like when you translate any other relationship with it's contrapositive, when translating the negation relationship you probably need to make a note that it could also mean both.
79 comments
Sometimes I feel like I learn more from the comment section.
@sebbotimpt Agreed. Often I read a section and go 'wait what about X?' and then someone who had the same problem as me explains it, or someone explains it to them. It's like a big, informal study group :D
#feedback I wish there was a diagram at the end of this lesson with all the conditionals and their negations. It would be helpful to have an overall visual comparison.
I just want to wish everyone the knowledge and determination to master all of this content and crush the LSAT!!
A few things for the structure of the intersectional relationships lessons --
1. can there be more visual representations
2. since the no contrapositive rule applies to all intersectional indicators, can it be right before the negation lesson-- (that also might highlight the distinction between negation and contrapositives better...)
3. can there be a final "value line" of where the bounds (lower and upper) of the statements apply -- i.e. None-some-------most------all. I think this helped me to best see the relationships among these intersectional indicators...
#feedback Yeah, I didn't even think of it until your comment, but the spacing between the negation and contrapositive lessons make it harder for those concepts to click and make it harder to recognize their distinction.
#feedback agreed. or even more mini quiz sections between these lessons to at least practice what we just went over
So negating isn’t saying no to the argument, it’s just saying “you forgot to look at it this way.” If you’re saying “it’s not the case that some unicorns poop rainbows,” then what you’re saying is there are no unicorns that poop rainbows. If not some, then none. You can’t say “if not some then most” because that’s not negating but adding onto the original claim. You can’t say “if not some then all” because again, that’s saying more than what the claim gives you evidence for.
Instead, negating is just saying “aha you forgot that there are some unicorns that DON’T poop rainbows!” A better view, for me, of negation is not “denying” or “negating” the original claim, but thinking of the possibilities that the claim didn’t originally consider.
@bdubbink2 this helped so muchhhh
Hi all, I made another flashcard set. This time for memorizing Quantifiers. Flashcards are what really helped me in undergrad and so I decided to make them to companion my 7sage studies. Thought I'd share to help others who would benefit :) made a folder that I will most likely add more sets to as I go. Much Love and happy studying! https://quizlet.com/user/ehoffmanwallace/folders/lsat-7sage-flashcards
@Elideebeep thats awesome thank you!
@MatthewJohnston sure thing!
So would the negation of Most Japanese whiskeys are expensive.
JW -m→ E be:
Zero to exactly half of Japanese whiskeys are expensive?
@Jcruzmed Yes
when you guys are negating do you actully find it helpful for questions because sometimes i feel like i am just getting tripped up
@garrettgrahm I find it most helpful for necessary assumption questions. Negating the ACs can help you determine which negation would destroy/weaken the argument (that would indicate the assumption that the argument depends on).
I'm confused why the negation for 'some' changed in this lesson. In the previous lesson, it was said that the negation of 'some' is 'none'. In this lesson, the example above "Some unicorns poop rainbows" is negated to "Some unicorns don't poop rainbows". I don't understand the distinction here, #help
The lesson says that "Some unicorns don't poop rainbows" is a "tempting but incorrect negation". The correct negation is identified as "No unicorns poop rainbows", which is the same as "None of the unicorns poop rainbows."
thank you so much for this clarification
confused why the some negative isn't the same as in previous lesson:
Original: P ←s→ C
Negated: /(P ←s→ C)
Negated: P → /C
Am I missing something? how the excerpt above become incorrect negation for unicorns and poop example?
This :U ←s→ /PR
Is Not the same as: /(UPR
Wait. Some unicorns poop rainbows is negated to No unicorns poop rainbows and is shown as (U->/PR). Wouldn't it be shown as /U->PR? This doesn't make total sense to me.
@AnnieCastillo remember group 4 indicators:
"No" would mean you have to negate a concept and make that concept the necessary condition. So "no unicorns poop rainbows" is equivalent to U->/PR.
/U->PR is the same as saying "if one is not a unicorn, then one poops rainbows.," which doesn't follow from the claim because we don't know anything about non-unicorns.
wait so are "some," "most, "many," quantifiers also conditionals? i.e. is "some unicorns dont poop rainbows" a conditional statement? or is it something completely different #help
@rc39 the quantifier words help identify the scope of the conditional. your if/then statement is your conditional, but the quantifier just specifies how often it occurs, or how much of any group is included within the conditional.
the statement "some unicorns don't poop rainbows" is a conditional statement, but the quantifier itself is not a conditional.
@tteokkim surgical explanation and i really appreciate it. you helped clarify some confusion working through this section. We may be looking at a conditional, but the quantifier is NOT conditional--it expresses an intersection. THANK YOU!
Can you negate most? The last example? #Help
I believe if you insert "It's not the case that..." then that should negate it. For example, the negation of "Most Japanese whiskeys are expensive" would be "It's not the case that most Japanese whiskeys are expensive", which establishes an upper bound of 50%.
same question! confused as to why it's mentioned #help
You could also imagine it as Not Most:
"Not Most Japanese whiskeys are expensive"
It might be confusing/ridiculous at first, but with practice it makes sense, lol.
Why is the negation of Some unicorns poop rainbows not no unicorns poop rainbows
BUT
Some mice are fat can be negated into no mice are fat or all mice are not fat?
I’m very confused on why this has changed. Please please help!
Or is the “tempting but incorrect negation” not saying that the above mentioned is incorrect, but the following statement is??? Lord, ima have a seizure 😂
@Bbqboi the negation of some unicorns poop rainbows is no unicorns poop rainbows
@Bbqboi yes exactly
@GennaBishop bless you 😂
@Bbqboi LOL they formatted it wrong because I was also confused when I first looked at it!
But they are saying the right negation is: No unicorns poop rainbows
and the incorrect negation is: Some unicorns don't poop rainbows.
@paligrrl bc I was STRESSING lol
What is an example of a question type we will encounter where having the negation of an intersection question is going to help us identify the correct answer?
^^^ in what cases should we negate on the test?
is this the correct negation of the most stamens provided as an example?
EX: Most Japanese whiskeys are expensive
original: Most J are E
negated: anywhere from 0 to half of J are E
English: anywhere from 0 to half of japeNeese whiskeys are expensive
Yes, that's right.
Any reason why the last example is not negated?
It's not the case that most Japanese whiskeys are expensive.
= 50% or less of Japanese whiskeys are expensive
(i think)
When talking about JW -m→ E, it says: "It could be true that as many as all Japanese whiskeys are expensive."
But earlier it was presented that all→most. #help
"All" must include "most," because it's everything. That is always the case when the term "all" is used. However, the range for "must" has a lower boundary of "more than half" and an upper boundary of "all."
So while it's possible that "most" is actually referring to "all," it is not always the case. Therefore, JW -m→ E, leaves the possibility that all Japanese whiskeys are expensive, but does not guarantee it.
All->most is a must be true. If all cats are cute, most cats must be cute, and some cats must be cute too.
But most->all is a could be true. If most cats are cute, definitely some cats are cute, but only possibly are all cats cute.
Must be true vs could be true
Very Helpful!
Helpful summary!
Is "few" a negation of "most"?
No, the negation of most is simply not most. There's a lesson where they go into it, but most implies in a hefty margin that something is greater than 50% and possibly by a larger share than that.
We can picture it on a rough scale of "50% < x <= 100%", where most is greater than half and can technically be all.
Few, on the other hand, implies that it is more than one (or possibly two, it's very vague) and less than one half. This is because few implies a really weird definition of "some but not many", a definition which highlights a more constricted view. With this, we can pinpoint a scale of "1 or 2 < x < many", with a rough indicator on your interpretation of many. However, this indication typically means it is less than half, so you could write the scale as "1 or 2 < x < 50%".
When looking at this, although a mathematical view could imply the negation of most as few, after all, "1 - 'most'" would leave you with a minority, there is a vague margin on what that would actually mean. As well, few is not inclusive to 1/2, meaning defining the negation of many as "few" would confuse an opposite for a negation.
Think back to the really early example of "the room is hot". The opposite of that statement would be "the room is cold", but would that be the negation? There's a range of temperatures that are not hot, like lukewarm, chilly, or freezing that aren't hot, and definitely aren't a strict cold. Because of this, the negation of "the room is hot" is simply "the room is not hot".
Think of the examples of most in a similar manner, where the negation of us saying "most penguins wear tuxedos" could not be "few penguins wear tuxedos". The language simply isn't inclusive to other possibilities, where no penguins wear tuxedos or exactly half of the penguins wear tuxedos. The only reasonable resolution is that it isn't the case that most penguins wear tuxedos.
TDLR: Few isn't inclusive to other possibilities in the range that the negation of most requires, but could be interpreted as an opposite, just not a negation.
Fellow gamecock on here. Comment was at the top of my screen. Just wanted to pay respect to the username!
Spurs up! Go cocks!!
can it be true to say that 'some' includes 'many' and 'all' and when negating they will all revert back to the same negation of 'none'?
no thats wrong
Some A are B- negation: no A are B
All A are B - negation: some A are B
Many A are B- negation: few A are B
^ I think thats accurate
wouldnt it be
All A are B – negation: some A are /B
since "all A are B" already includes the possibility of "some A are B" (because some could include all), so your answer would not entirely negate it.
additionally, I think that "many A are B" negated is just /(A ‑m→B), or, "it is not the case that many A are B". This way it doesn't necessitate that some A are not B, as the word "few" would.
Any feedback is appreciated :)
What's the difference between a negation and a contrapositive?
The contrapositive of a conditional statement is created by flipping the order of the statement and negating both parts. It is logically equivalent to the original — meaning if one is true, so is the other.
On the other hand, negation simply means stating that the original statement is not true. It is not logically equivalent — instead, it expresses the opposite.
So, while the contrapositive preserves the truth of the original statement, negation challenges or contradicts it.
I still have a question. Do "all" statements always negate differently than group 1 conditional indicator statements? From my understanding of the material, this is how an all statement negates:
A some arrow /B
And this is how a conditional statement negates:
A and /B
But I think where I'm still confused is whether these are interchangeable since all is a group 1 indicator? I just want to know, if I see a group 1 indicator or an all statement on the LSAT, which translation I should use to get the right answer of if using either is fine.
During the skill builder exercises, the all statements where negated with both the some arrow and the and /, so I am guessing he's trying to say that both are correct. Like when you translate any other relationship with it's contrapositive, when translating the negation relationship you probably need to make a note that it could also mean both.
#feedback Can you translate the negation of the word "rarely" (not rarely) to "frequently"?